The Liapunov Center Theorem for a Class of Equivariant Hamiltonian Systems

Jia Li and Yanling Shi

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: We consider the existence of the periodic solutions in the neighbourhood of equilibria for C∞ equivariant Hamiltonian vector fields. If the equivariant symmetry S acts antisymplectically and S2 = I, we prove that generically purely imaginary eigenvalues are doubly degenerate and the equilibrium is contained in a local two‐dimensional flow‐invariant manifold, consisting of a one‐parameter family of symmetric periodic solutions and two two‐dimensional flow‐invariant manifolds each containing a one‐parameter family of nonsymmetric periodic solutions. The result is a version of Liapunov Center theorem for a class of equivariant Hamiltonian systems.

Date: 2012
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https://doi.org/10.1155/2012/530209

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:530209

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